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Some applications of \(K\)-theory to framed bordism: E-invariant and transfer. (English) Zbl 0982.55500

Bonn: Univ. Bonn, Mathematisch-Naturwissenschaftliche Fakultät (Habil.), 115 p. (1979).
From the introduction: We study \(\pi^S_*(P_\infty\mathbb{C})\) using as the main tools the \(e\)-invariant of Adams and various transfer maps. The \(e\)-invariant describes the information about \(\pi^S_*(X)\) obtainable using \(K\)-theory and the transfer maps relate \(\pi^S_*(P_\infty\mathbb{C})\) to the stable homotopy of spheres and allow us to construct elements in \(\pi^S_*(P_\infty\mathbb{C})\).

MSC:

55Q10 Stable homotopy groups
55Q52 Homotopy groups of special spaces
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